A Study on Urban Comprehensive Carrying Capacity from the Perspective of “Production–Living–Ecological Space” Based on Grey Clustering Analysis and TW-FE: A Case Study of China’s Three Northeastern Provinces

Research on Urban Comprehensive Carrying Capacity (UCCC) from the perspective of Production–Living–Ecological Spaces (PLES) can provide new insights for enhancing carrying capacity and offer decision-making references for sustainable urban development. Taking China’s three northeastern provinces as an example, this study, based on the PLES perspective, constructs an evaluation indicator system for UCCC. Combining the MEREC method and Grey Clustering Analysis, it assesses the UCCCs of the three northeastern provinces and analyzes the spatiotemporal evolution characteristics and coupling coordination patterns. On this basis, a Two-Way Fixed-Effects model (TW-FE) and a threshold panel model are employed to identify the key factors influencing the UCCCs and analyze the mechanism through which these factors affect the UCCCs. The research findings indicate the following: (1) From 2014 to 2023, the UCCCs in the three northeastern provinces showed an overall steady increase. The UCCC of Liaoning Province consistently remained higher than those of Jilin and Heilongjiang Provinces. In terms of the internal structure of the PLES, the Living Space Carrying Capacity (LSCC) was higher than the Production Space Carrying Capacity (PSCC) and Ecological Space Carrying Capacity (ESCC), serving as the primary driving force for the UCCC. (2) The UCCCs in the three northeastern provinces exhibited significant spatial heterogeneity. The UCCCs of Shenyang, Dalian, Changchun, and Harbin were higher than those of surrounding cities. The global Moran’s I indicated that strong spatial dependence had not yet formed, and regional synergy mechanisms remained weak. The local Moran’s I revealed that the spatial aggregation pattern displayed dynamic changes. (3) The coupling coordination degrees of the carrying capacities of the PLES in the three northeastern provinces and each of their prefecture-level cities still did not reach the “Barely Coordinated” stage during the study period. (4) The key influencing factors for the overall UCCCs in the three northeastern provinces were the Degree of Openness to the Outside World (DOOW), Financial Development Level (FDL), and Economic Development Level (EDL). The key influencing factors for the UCCCs differed among Liaoning, Jilin, and Heilongjiang Provinces, and these key factors exhibited a nonlinear effect on the UCCCs.